Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European-style and American-style Asian options and for discretely and continuously monitored versions. In the present paper we focus on the European-style Asian options. The exponential convergence rates of Fourier cosine expansions and Clenshaw–Curtis quadrature reduces the CPU time of the method to milliseconds for geometric Asian options and a few seconds for arithmetic Asian options. The method’s accuracy is illustrated by a detailed error analysis and by various numerical examples.